2x the initial cost seems reasonable. If the estimate was this wrong, it's useless and the project needs to be reestimated.
The problem is that many initial estimates will be low ball offers to try and win a contract. Perhaps combine the sunken-cost-limit with delayed payments, otherwise companies might low ball offers knowing they can never finish but still don't care because they'll be paid.
Better oversight is clearly needed too. There won't be one tool that'll do the job on its own.
The funny thing is, many projects (and I should have omitted government-run, any organization can suffer from this problem) have reasonable cost estimates when they begin. Why not start with those? Perhaps this rule would incentivize more realistic estimates?
The contractors have all the incentives to extract as much government money as they possibly can during the entire process.